Bernoulli

  • Bernoulli
  • Volume 7, Number 6 (2001), 913-934.

Mixed fractional Brownian motion

Patrick Cheridito

Full-text: Open access

Abstract

We show that the sum of a Brownian motion and a non-trivial multiple of an independent fractional Brownian motion with Hurst parameter H ∈ (0,1] is not a semimartingale if H ∈ (0, ½) ∪ (½, ¾], that it is equivalent to a multiple of Brownian motion if H = ½ and equivalent to Brownian motion if H ∈ ( ¾ , 1]. As an application we discuss the price of a European call option on an asset driven by a linear combination of a Brownian motion and an independent fractional Brownian motion.

Article information

Source
Bernoulli, Volume 7, Number 6 (2001), 913-934.

Dates
First available in Project Euclid: 10 March 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1078951129

Mathematical Reviews number (MathSciNet)
MR1873835

Zentralblatt MATH identifier
1005.60053

Keywords
equivalent measures mixed fractional Brownian motion semimartingale weak semimartingale

Citation

Cheridito, Patrick. Mixed fractional Brownian motion. Bernoulli 7 (2001), no. 6, 913--934. https://projecteuclid.org/euclid.bj/1078951129


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